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Congruency Theorems/Postulates (“shortcuts”)

Congruency Theorems/Postulates (“shortcuts”). Objective: use shortcuts to determine if two triangles are congruent How can we tell if two triangles are congruent without knowing all of its information?. 7 0 °. 14 ft. 12 ft. 80 °. 30 °. 13.5 ft.

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Congruency Theorems/Postulates (“shortcuts”)

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  1. Congruency Theorems/Postulates (“shortcuts”) Objective: use shortcuts to determine if two triangles are congruent How can we tell if two triangles are congruent without knowing all of its information?

  2. 70° 14 ft 12 ft 80° 30° 13.5 ft

  3. What’s the LEAST AMOUNT of information needed in order to determine that two triangles MUST be congruent?

  4. If I am told that all of the SIDES are congruent… does that mean all of the ANGLES are congruent?

  5. YES! Postulate #1: Side-Side-Side (SSS) If 3 sides of one triangle are congruent to 3 sides of another triangle, the triangles must be congruent

  6. If I am told that all of the ANGLES are congruent… Does that mean all of the SIDES are congruent?

  7. NO

  8. If I am told that TWO SIDES and the ANGLE BETWEEN THEM are congruent… Does that mean that the other sides & angles are congruent?

  9. YES! Postulate #2: Side-Angle-Side (SAS) If two sides and the angle between them are congruent, then the triangles are congruent

  10. If I am told that TWO SIDES and an ANGLE NOT BETWEEN THEM are congruent… Does that mean that the other sides & angles are congruent?

  11. NO! • The triangles do not have to be congruent

  12. If I am told that TWO ANGLES and ONE SIDE are congruent… Does that mean that the other sides & angles are congruent?

  13. YES! Postulate #3: Angle-Side-Angle (ASA) If two angles and the side between them are congruent, then the triangles must be congruent

  14. Theorem #4: Angle-Angle-Side (AAS or SAA) If two angles and a side not between them are congruent, then the triangles are congruent

  15. Theorem # 5: Hypotenuse-Leg (HL)If two legs of RIGHT TRIANGLE and their hypotenuses are congruent, then the triangles are congruentHypotenuse: the side across from the right angle

  16. YES! NO! SSS SAS ASA AAS HL AAA SSA (*ASS)

  17. Ex 1) SSS

  18. Ex 2) SAS

  19. Ex 3) AAS

  20. Ex 4) ASA

  21. Ex 5) HL

  22. Can you prove it? Why?

  23. Can you prove it? Why?

  24. Can you prove it? Why?

  25. Can you prove it? Why?

  26. Can you prove it? Why?

  27. Can you prove it? Why?

  28. Can you prove it? Why?

  29. Can you prove it? Why?

  30. Can you prove it? Why?

  31. Can you prove it? Why?

  32. Can you prove it? Why?

  33. Can you prove it? Why?

  34. Show me SSS

  35. Show me SAS

  36. Show me AAS

  37. Show me ASA

  38. Show me HL

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